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Weighted Lim’s geometric mean of positive invertible operators on a Hilbert space
Author(s)
Ploymukda, Arnon
Date Issued
March 1, 2020
Type
Article
Abstract
We generalize the weighted Lim’s geometric mean of positive definite matrices to positive invertible operators on a Hilbert space. This mean is defined via a certain bijection map and parametrized over Hermitian unitary operators. We derive an explicit formula of the weighted Lim’s geometric mean in terms of weighted metric/spectral geometric means. This kind of operator mean turns out to be a symmetric Lim-Pálfia weighted mean and satisfies the idempotency, the permutation invariance, the joint homogeneity, the self-duality, and the unitary invariance. Moreover, we obtain relations between weighted Lim geometric means and Tracy-Singh products via operator identities.
Citation
Journal of Computational Analysis and Applications, 29(2), 390-400, 2020